I want to briefly examine what a universal morality is, and in particular, what we mean by "universal." Some possibilities include: a morality that is actually practiced by everyone; one that is internally consistent; or one that "ought to" be practiced by everyone, i.e., it is objectively correct.
The first possibility is straightforward to dismiss. Even in eras and venues where overall conformity to particular moral scruples is high, there has always been non-compliance, both intentional and unintentional. Perhaps more illuminating, one is unlikely to find even a single individual who with absolute consistency practices his own moral code. Though this empirical observation does not prove its impossibility, practice is surely our least promising notion of moral universality.
In contrast, it is easy to show that internal consistency is possible. Nihilism, the complete absence of values, is the simplest example, though vacuous. The categorical imperative, "always act in such a way that the maxims of your will could function as the basis of a universal law of action" enshrines the notion of logical consistency itself as the fundamental principle. However, alone it provides no actual prescriptions, and puts the burden of determining those prescriptions on the individual. Surely not all, and possibly no, individuals are capable of fully analyzing the question of "what could function the basis of a universal law." Further, even with such analysis, wildly divergent views such as "murder everyone I see" and "never harm a soul" both can function as universal laws.
Just as damaging, discerning what components of actions are "maxims of will" and which are mere particulars is an abstractive process that is subject to both error and subjective interpretation. Thus individuals will come to different conclusions and there will be a wide diversity of actual practice.
These examples, which are not merely examples but shining historical attempts to find universality, suggest that logical consistency may be necessary but is probably not sufficient for anything we could reasonably call a universal morality. If the maxim results in very little consistency in practice, it is a merely theoretical exercise that misses the point of practical reason.
Moving on to address the proposal of moral codes that are objectively correct, I enlist the notion of risk profile. While moral problems are often posed in a context of perfect predictability, we humans are never faced with such crisp decision opportunities. Instead, it is necessary to make decisions based on probability distributions and outcome valuations. While these distributions are subject to knowledge limitations, that is not the primary difficulty. Instead, even given an agreed probability distribution and outcome valuation profile, different subjects will prefer different choices. Whether caused by innate inclinations or developmental desires, some individuals are comfortable taking risky actions with the appropriate compensation, while others are more comfortable with the security and lower likely compensation of a less risky choice.
This variation is not subject to an objective determination. As long as risk levels are rationally compensated, one cannot choose among the options without subjective risk profile context. Further, zero risk and unlimited risk approaches are neither possible nor sustainable. Thus any attempt to "draw a line" will have an arbitrary flavor. I conclude that there is no objectively correct universal ethics.